Problem: Reduce to lowest terms: $ \dfrac{7}{5} \div - \dfrac{7}{5} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{5}$ is $- \dfrac{5}{7}$ Therefore: $ \dfrac{7}{5} \div - \dfrac{7}{5} = \dfrac{7}{5} \times - \dfrac{5}{7} $ $ \phantom{ \dfrac{7}{5} \times - \dfrac{5}{7}} = \dfrac{7 \times -5}{5 \times 7} $ $ \phantom{ \dfrac{7}{5} \times - \dfrac{5}{7}} = \dfrac{-35}{35} $ The numerator and denominator have a common divisor of $35$, so we can simplify: $ \dfrac{-35}{35} = \dfrac{-35 \div 35}{35 \div 35} = -1 $